Let's solve the expression step by step:

Given expression:
\[
2.40 \times 0.75 + \frac{5}{20} : \frac{2}{40}
\]

### Step 1: Simplify \(2.40 \times 0.75\)
\[
2.40 \times 0.75 = 1.8
\]

### Step 2: Simplify \(\frac{5}{20}\)
\[
\frac{5}{20} = 0.25
\]

### Step 3: Simplify \(\frac{2}{40}\)
\[
\frac{2}{40} = 0.05
\]

### Step 4: Divide \(\frac{5}{20}\) by \(\frac{2}{40}\)
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
0.25 \div 0.05 = 0.25 \times 20 = 5
\]

### Step 5: Substitute back into the expression
\[
1.8 + 5
\]

### Step 6: Perform the addition
\[
1.8 + 5 = 6.8
\]

The final answer is:
\[
\boxed{6.8}
\]

Would you like more details or have any questions?

Here are 8 related questions:
1. How do you simplify fractions?
2. What is the reciprocal of a fraction, and why is it useful?
3. How do you multiply decimals?
4. What are the rules for dividing fractions?
5. How would the expression change if the numbers were different?
6. What happens when you multiply a fraction by a whole number?
7. Can you provide another example with division of fractions?
8. Why is it important to understand the order of operations?

**Tip:** When dividing fractions, always multiply by the reciprocal of the divisor to simplify the expression correctly!

Learn how to solve the expression 2.40 * 0.75 + 5/20 : 2/40 step-by-step with detailed explanations. This problem covers key concepts in decimals, fractions, and order of operations. Suitable for students in Grades 6-8.

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